Development of regularization modeling and error-control in large-eddy simulation

Numerical simulation is developing into a viable research-tool to help understand dispersion and structure in turbulence. In order to make progress toward simulating flows under realistic flow-conditions and in complex flow-domains, large-eddy simulation appears an essential stepping-stone. This requires a combination of accurate numerical treatment and proper (subgrid) modeling of the dynamic effects of small-scale turbulence. It will be shown that accurate subgrid models may be systematically derived from mathematical regularization principles. This will be illustrated for the Leray and \mbox{NS-$\alpha$} models. Moreover, a database analysis of interacting modeling and simulation errors in large-eddy simulation will be discussed in terms of error-landscapes. The optimality of the dynamic procedure will be quantified and a new inverse polynomial interpolation method will be proposed with which model parameters can be optimized to approximate the `optimal refinement strategy'